Southampton striker Che Adams scored against his former club, and midfielders Stuart Armstrong and Nathan Redmond struck after the interval as it beat Sheffield United 3-0 at St Mary's Stadium on Sunday to go third in the table.
Southampton dominated possession and went ahead on 34 minutes as the Blades failed to properly deal with a James Ward-Prowse free kick and Adams reacted quickest to tap home his fourth league goal of the season in front of 2,000 supporters.
Armstrong doubled the home side's lead in the second half with a low shot that gave Blades goalkeeper Aaron Ramsdale no chance as it took a big deflection off defender Phil Jagielka and rolled into the net.
Substitute Redmond scored his first goal of the season seven minutes from time with a side-footed finish following an exchange with midfielder Oriol Romeu to heap the pressure on Chris Wilder's bottom-placed side.
“We knew it would be a tough one. They're quite defensive. We knew that they would want to get something from the game,” Armstrong said in a post-match interview.
“It was important to get that breakthrough early on. The first few minutes of the second half were a bit difficult, but we found our feet and deserved the win.
“Ultimately we want to be at the top end of the table. We've found ourselves in the bottom half in recent years... We take things game by game, but today's a good start.”
The Blades' 11th defeat of the campaign makes them the first team since Queens Park Rangers in 2012 to be without a win after 12 Premier League matches, and pressure is mounting on manager Wilder to arrest their slide.
Ralph Hasenhuettl's Southampton climbed to third in the table behind leader Tottenham Hotspur and Liverpool with 23 points from 12 games ahead of a potentially tricky clash at Arsenal on Wednesday.
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